A camera shop stocks six different types of batteries, one of which is type A7b. Suppose that the camera shop has only twelve A7b batteries but at least twenty of each of the other types. Now, choose the correct answer for the following question - How many ways can a total inventory of twenty batteries be distributed among the six different types? C(24, 20) - C(12,7) C(25, 20) - C(12,7) C(20, 15) - C(13,7) C(25, 20) - C(13,7)

Since the assumption that the vis are linearly dependent is false as a result of this contradiction, they are in fact linearly independent.

If no vector in a collection of vectors can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others. If you write a collection of vectors as the columns of the matrix A and solve Ax = 0, you can tell if the vectors are linearly independent. The vectors are linearly dependent if there are any non-zero solutions. They are linearly independent if x = 0 is the sole viable answer.

You want to show v1,…,vn are linearly independent.

Suppose they are not.

Then there are scalars c1,…,cn (not all zero) so that c1v1+…+cnvn=0. Then

T(c1v1+…+cnvn)=T(0)=0.

So c1T(v1)+…+cnT(vn)=0, which means that T(v1),…,T(vn) are not linearly independent.

This contradiction means the assumption that the vis are linearly dependent is false, so they are indeed linearly independent.

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Colleen's average rate over the last 9 hours of her trip is 81 miles / 9 hours = 9 miles per hour.

1. To find the average rate, we need to divide the total distance traveled in the last 9 hours by the time taken.
2. In the first 2 hours, Colleen traveled 20 miles, so in the next 9 hours, she traveled 101 - 20 = 81 miles.
3. Therefore, her average rate over the last 9 hours is 81 miles / 9 hours = 9 miles per hour.

Therefore, Colleen's average rate over the last 9 hours of her trip is 81 miles / 9 hours = 9 miles per hour.

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The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

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Answer:

Step-by-step explanation:

10 inches

Answer:

68.5 inches

Step-by-step explanation:

The pythagorean theorem is a^2+b^2 = c^2

In this case, a = 60, b = 33, and we are looking for c, so this is how you do it:

60^2 + 33^2 = 3600 + 1089 = 4689

sqrt(4689) = 68.47627326...

Rounded to the nearest tenth is 68.5!

The center is (-6, -5) and the radius is approximately 15.3624 units. To find the center and radius of the circle with equation x^2 + 12x + y^2 + 10y - 164 = 0.

We need to rewrite the equation in standard form:

(x^2 + 12x) + (y^2 + 10y) = 164

Completing the square for each variable inside the parentheses, we add and subtract the appropriate constant values to both sides of the equation:

(x^2 + 12x + 36 - 36) + (y^2 + 10y + 25 - 25) = 164 + 36 - 25

(x + 6)^2 - 36 + (y + 5)^2 - 25 = 175

Simplifying further, we get:

(x + 6)^2 + (y + 5)^2 = 175 + 36 + 25

(x + 6)^2 + (y + 5)^2 = 236

Comparing this equation to the standard form of a circle,

(x - h)^2 + (y - k)^2 = r^2,

we can see that the center of the circle is (-6, -5) and the radius is sqrt(236), or approximately 15.3624 units. Therefore, the center is (-6, -5) and the radius is approximately 15.3624 units.

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The speed of the particle when it is moving parallel to the y-axis is approximately 17.88 m/s.

When the particle moves parallel to the y-axis, its velocity component in the x-direction is zero. Therefore, we need to find the value of t for which the x-component of the velocity becomes zero.

Given that the x-component of the velocity is (2t - 8), we set it equal to zero and solve for t:

2t - 8 = 0

2t = 8

t = 4

At t = 4 seconds, the particle is moving parallel to the y-axis. To determine the speed of the particle at this instant, we calculate the magnitude of its velocity:

v = √[(2t - 8)^2 + ((2/t^2) - 18)^2]

v = √[(2(4) - 8)^2 + ((2/(4^2)) - 18)^2]

v = √[0^2 + ((2/16) - 18)^2]

v = √[0 + (-17.875)^2]

v ≈ 17.88 m/s

Therefore, the speed of the particle when it is moving parallel to the y-axis is approximately 17.88 m/s.

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Answer:

if im not mistaken its 143

The concept is the Vertical Lines. The Vertical Lines are a pair of opposing, congruent angles created by intersecting lines. It is option A.

An upward line is a line on the direction plane where every one of the focuses on the line have a similar x-coordinate. Because they are perpendicular to the ground and extend toward the sky, vertical lines frequently convey a sense of height.

At the point when two straight lines cross each other vertical points are shaped. Every vertical angle is equal and congruent.

By super-imposing the two pairs of non-adjacent angles created by intersecting two lines, vertical angles are congruent.

Every vertical angle has the same length. We call angles congruent when their measurements are the same.

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Question:

Which of coming up next is best depicted as a couple of inverse points shaped by crossing lines?

A. Vertical angles

B. Supplementary angles

C. Complementary angles

D. Linear pair

The value of the angle R in the right triangle PQR is sin⁻¹ 6 / 8

The situation forms a right angle triangle.

The angle R can be found as follows:

using trigonometric ratios,

sin R = opposite / hypotenuse

Therefore,

opposite sides = 6

hypotenuse = 8

sin R = 6 / 8

R = sin⁻¹ 6 / 8

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The value of angle A is 100⁰.

option D is the correct answer.

The measure of angle A is calculated by applying the following formula as shown below;

If line AB is similar to line AC, then angle B must be equal to angle C.

∠ B = ∠ C = 40 ⁰

The value of angle A is calculated as follows;

∠ A = 180⁰ - ( ∠ B + ∠ C ) ( sum of angles in a triangle )

∠ A = 180⁰  -  ( 40⁰ + 40⁰ )

∠ A = 180⁰ - ( 80 ⁰ )

∠ A = 100⁰

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Answer: x-intercept(s): (7/5, 0)

Y intercept(s): (0,−7)

Answer: 1/7

Step-by-step explanation:

From the question, we are informed that it takes Deanna seven hours to paint a fence. The fraction of the fence does she paint in one hour will be one divided by seven hours which can mathematically be written as:

= 1/7

This means that she'll paint 1/7 of the fence in 1 hour.

The following are the offered rational exponents in expression form:

• (A) the fourth root's tenth root = \(\sqrt[10]{4}\)

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: The following rational exponents are expressed in the expression form (Math Operator, Number/Variable, Math Operator): (A) the tenth root of four= \(\sqrt[10]{4}\)

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Answer:

Marty's with a slope of 1/3

Step-by-step explanation:

The functions Marty and Ethan wrote are analyzed the find the slope of each of the function

The equation Marty wrote is presented here as follows;

\(y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right)\)

Marty's equation can be written in slope and intercept form, y = m·x + c, as follows;

\(y = \dfrac{1}{3} \cdot\left (x + 9 \right) - 3\)

\(y = \dfrac{1}{3} \cdot x + \dfrac{9}{3} \right) - 3 = \dfrac{1}{3} \cdot x + 0\)

\(y = \dfrac{1}{3} \cdot x\)

By comparison, the slope of the function, m = 1/3

\(\therefore \ the \ slope \ of \ Marty's \ function, \ y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right), \ m =\dfrac{1}{3}\)

Marty's function has a slope of m = 1/3

Ethan has the following two column table;

\(\begin{array}{rl}x&y\\-4&9.2\\-2&9.6\\0&10\\2&10.4\end{array}\)

The slope, m, of the data in the above table is given as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Taking any two points, (x₁, y₁) = (-4, 9.2), and (x₂, y₂) = (2, 10.4), we get;

\(Slope, \, m =\dfrac{10.4-9.2}{2-(-4)} = \dfrac{1.2}{6} = \dfrac{1}{5}\)

Ethan's function has a slope of m = 1/5

Therefore;

Marty's slope of 1/3 is larger, given that 1/3 > 1/5.

Answer:

C. Marty’s with a slope of 1/3

Step-by-step explanation:

Did the test and got it correct

Answer:the answer is option a. it involves organizing events in the order in which they occurred.

Step-by-step explanation:

Answer:

-5 , 3 , 11 , 19 , 27

Step-by-step explanation:

typing bc I need to have 20 letters

The market value of 320 shares is Nu 21120.

Market value of 320 shares

The market value of 320 shares bought by a man is to be determined provided the face value of each share is Nu 50 and the premium is 20% and the company gives a dividend rate of 12%.

First, let's define what a premium is. A premium is the amount by which something, like a stock, bond, or commodity, is above its issue price.

It is the extra amount that an investor pays to purchase the security.

In this case, the premium is 20% of the face value, which means it's 20/100 x Nu 50 = Nu 10 per share.

The cost per share for the buyer, therefore, is Nu 50 + Nu 10 = Nu 60 per share.

Now, we can determine the cost of 320 shares as: Cost of 320 shares = Nu 60 x 320= Nu 19200

Next, let's calculate the dividend earned by the buyer.

Dividend rate is given as 12% and since the face value of each share is Nu 50, the dividend paid per share is 12/100 x Nu 50 = Nu 6.

Therefore, the total dividend earned by the buyer is: Dividend earned = 320 x Nu 6= Nu 1920

Now, let's calculate the market value of the shares.

Market value of the shares is the total value of the shares if they were sold in the market.

We can determine this by adding the cost of the shares to the dividend earned.

Market value of 320 shares = Cost of 320 shares + Dividend earned= Nu 19200 + Nu 1920= Nu 21120

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Answer:

130

Step-by-step explanation:

Form a simple equation:

x/100 = 1.3

x= 1.3 * 100

x = 130

GIVE BRAINLIEST PLEASE ITS MY BIRTHDAY

Answer:

130

Step-by-step explanation:

Just like before, do the opposite and multiple by 100

1.3 * 100 = 130

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

Answer:

7474747448548

Step-by-step explanation:

I hope this helps

The derivative of f(x) = x^2 * sin(x) is f'(x) = 2x * sin(x) + x^2 * cos(x). One real-life application of the product rule is in economics and business analysis when determining the optimal production level to maximize profit.

Title: Product Rule for Derivatives

Key Vocabulary and Notation:

Derivative: The rate of change of a function with respect to its independent variable.

Product Rule: A rule in calculus used to differentiate the product of two functions.

f(x) and g(x): Two differentiable functions of x.

f'(x) and g'(x): The derivatives of f(x) and g(x), respectively.

The Process of the Product Rule:

The product rule is a formula used to find the derivative of the product of two functions. It is commonly written as:

(d/dx)(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)

Here's the step-by-step process of applying the product rule:

Identify the two functions: Let f(x) and g(x) be the two functions that we want to find the derivative of their product, f(x)g(x).

Calculate the derivative of f(x): Find the derivative of f(x) with respect to x and denote it as f'(x).

Calculate the derivative of g(x): Find the derivative of g(x) with respect to x and denote it as g'(x).

Apply the product rule: Plug the values of f'(x) and g'(x) into the product rule formula:

(d/dx)(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)

Simplify the expression: Perform any necessary algebraic simplifications to obtain the final derivative expression.

Worked Example:

Let's use the product rule to find the derivative of the function f(x) = x^2 * sin(x).

Step 1: Identify the functions:

f(x) = x^2 and g(x) = sin(x)

Step 2: Calculate the derivative of f(x):

f'(x) = 2x

Step 3: Calculate the derivative of g(x):

g'(x) = cos(x)

Step 4: Apply the product rule:

(d/dx)(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)

(d/dx)(x^2 * sin(x)) = (2x * sin(x)) + (x^2 * cos(x))

Step 5: Simplify the expression:

(d/dx)(x^2 * sin(x)) = 2x * sin(x) + x^2 * cos(x)

Therefore, the derivative of f(x) = x^2 * sin(x) is f'(x) = 2x * sin(x) + x^2 * cos(x).

Example of Real-Life Application:

One real-life application of the product rule is in economics and business analysis when determining the optimal production level to maximize profit. Consider a scenario where the profit of a company is given by the product of the price per unit (p) and the quantity produced (q), denoted by P = p * q.

To find the rate at which profit changes with respect to the quantity produced, we can use the product rule. The derivative of the profit function, dP/dq, represents the marginal profit, indicating the additional profit earned by producing one more unit.

By applying the product rule and differentiating the profit function with respect to quantity, we can analyze how changes in price and quantity affect the company's profit and make informed decisions about production levels to maximize profitability.

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Answer:

-2X=O

X=0

THE ANSWER IS X=0

Step-by-step explanation:

Hopes it helps

Answer:

6 Slices

Step-by-step explanation:

Total units = 1 + 3 + 2 = 6 Units

6 Units = 18 Slices of Pizza

Iris shared 2 units.

1 Unit = 18/6 = 3 Slices of Pizza

2 Units = 2 * 3 = 6 Slices of Pizza

Answer:

60 miles per hour

Step-by-step explanation:

We need to simply divide the total distance he traveled by the total time it took him.

At 10:00 AM, he is 200 miles from New York.

At 12:00 PM, he is 80 miles from New York.

This means that 2 hours has elapsed and the distance he has traveled is:

200 - 80 = 120 miles

Therefore, his average speed is:

120 / 2 = 60 miles per hour

The answer is low using correlation.

What is correlation?

The terms "co" and "relation" are combined to form the word "correlation." Correlation is the relationship between any set of data when taken as a whole because the term "co" signifies together.

The correlation coefficient, which in statistics is a number between -1 and +1, measures the linear dependency of the collection of data.

It cannot capture nonlinear correlations between two variables and only assesses the magnitude and direction of the linear link between the two variables.

The difference between dependent and independent variables is not possible.

In the question, it is given that there is a high positive correlation between x and y, which means for every increase in x there is a corresponding increase in y

So if x is having low score, than y is also having low score

Hence the answer is low.

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If a hospital medical unit has 50 beds and the unit provided 1,420 days of service, the average daily census for the medical unit in May is 28.4.

To find the average daily census for a medical unit in May, we divide the total number of days of service provided by the number of beds in the unit. Here's how we do it:

According to the question, Total number of beds = 50 and Total number of days of service = 1,420

Average daily census = Total number of days of service / Total number of beds

Average daily census = 1,420/50

Average daily census = 28.4

Therefore, the average daily census for the medical unit in May is 28.4.

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Answer:

a is not equivalent to b and c.

Step-by-step explanation:

a.

\(50( {2}^{x + 2} ) = 25 \times 2( {2}^{x + 2} ) = 25( {2}^{x + 3} )\)

b.

\(25( {2}^{2x + 1} ) \)

c.

\(50( {4}^{x} ) = 50( { {2}^{x} )}^{2} = 50( {2}^{2x} ) = 25 \times 2( {2}^{2x} ) = 25( {2}^{2x + 1} )\)

Step-by-step explanation:

-3 +(-3)

= -3 -3

True because (+)(-) = -

The place with the best buy between village market and Sam's club is Sam's club at $0.59 per can.

Village market:

Unit rate = Total cost / green beans

= 3.70 / 5

= $0.74 per can

Sam's club:

Unit rate = Total cost / green beans

= 5.90/10

= $0.59 per can

Therefore, the place with the best buy between village market and Sam's club is Sam's club at $0.59 per can.

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The magnitude of the net electric field at point P due to the particle is 0 . explanation is given as

let us assume that , The charges of the four particles and the distance are given then on understanding the  concept of electric field  at electrostatics concept. on using the concept of the electric field at any given point, then production of  individual electric field by a charge. and we known the concept of superposition law, on applying the law  we  get the value of the electric field in its direction and this shows the determination of   the net electric field at that point.

The magnitude of the electric field,  

E = q * R

where R = The distance of field at  point from the charge, and q = charge of the individual particle

According to the superposition principle, the electric field at a single point due to more than one charges present ,hence on calculation of net electric field  we get the origin of the coordinate system  which is placed at point P and the y-axis is situated and oriented in the direction of the charge,  (passing through the charge, ). The x-axis which  is perpendicular to the y axis, and thus passes through the identical charges, then the  individual magnitudes of an electric field is due to the charges are demonstrated by using the absolute signs of the charges. Now let us assume that the point charge which  being positive i.e  ( q > 0), we can see that the contributions coming from each charge gets cancel to each other. Therefore the net electric field in the direction of the y-axis is given using equation as  E= 0

hence the net electric field is zero .

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